Invarient Subspaces Of Hardy Classes On Infinitely Connected Open Surfaces

Invariant Subspaces of Hardy Classes on Infinitely Connected Open Surfaces

We generalize Beurling's theorem on the shift invariant subspaces of Hardy class H[superscript]2 of the unit disk to the Hardy classes of admissible Riemann surfaces. Essentially, an open Riemann surface is admissible if it admits enough bounded multiple valued analytic functions. The class of admissible surfaces contains many infinitely connected surfaces, and all finite surfaces, but does not contain all plane regions admitting sufficiently many bounded analytic functions to sseparatepoints. We generalize the ttheorem of A.H. Read and the Cauchy integral formula to the boundary values, on the Hayashi boundary, of functions in the Hardy classes of admissible surfaces.

Invariant Subspaces of Hardy Classes on Infinitely Connected Open Surfaces

Hardy Classes on Infinitely Connected Riemann Surfaces